A new auxiliary particle method for the Hubbard, t-J and Heisenberg models

A new bond auxiliary particle method for the Hubbard, t-J and Heisenberg Hamiltonians is presented. First, the one-dimensional (1D) Heisenberg Hamiltonian is studied as a test case. The exact ground state is approached rapidly via perturbation theory. At the level of second-order perturbation theory, the ground state energy is accurate within a few per cent, while in the 15th order it is accurate to five figures. Without any renormalization, the spin velocity is given with 10% accuracy, and the spectrum is correctly gapless. The degeneracy is also correct, giving a Wilson ratio R=2. The method is used to calculate analytically the full Green's function for a single hole in a half-filled (one electron per site) t-J model.